Systems of Linear Equations

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Front

What does it mean if a system of equations has no solution?

Back

It means that the lines represented by the equations are parallel and will never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

How can you determine if a system of equations has exactly one solution?

Back

If the lines represented by the equations intersect at exactly one point, the system has exactly one solution.

Front

What is the graphical representation of a linear equation?

Back

A linear equation can be represented graphically as a straight line on a coordinate plane.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the intersection point of two lines?

Back

To find the intersection point, solve the system of equations simultaneously to find the values of x and y.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients determine the slope and position of the line on the graph.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, which can be either one solution or infinitely many solutions.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines.